Problem: Simplify the following expression: $ a = \dfrac{5}{-4p + 6} - \dfrac{-6}{5} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5}{5}$ $ \dfrac{5}{-4p + 6} \times \dfrac{5}{5} = \dfrac{25}{-20p + 30} $ Multiply the second expression by $\dfrac{-4p + 6}{-4p + 6}$ $ \dfrac{-6}{5} \times \dfrac{-4p + 6}{-4p + 6} = \dfrac{24p - 36}{-20p + 30} $ Therefore $ a = \dfrac{25}{-20p + 30} - \dfrac{24p - 36}{-20p + 30} $ Now the expressions have the same denominator we can simply subtract the numerators: $a = \dfrac{25 - (24p - 36) }{-20p + 30} $ Distribute the negative sign: $a = \dfrac{25 - 24p + 36}{-20p + 30}$ $a = \dfrac{-24p + 61}{-20p + 30}$ Simplify the expression by dividing the numerator and denominator by -1: $a = \dfrac{24p - 61}{20p - 30}$